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Question
Find the value of k if M = `[(1,2),(2,3)]` and `M^2 - km - I_2 = 0`
Solution
`M^2 = [(1,2),(2,3)][(1,2),(2,3)] = [(1+4, 2+6),(2+6,4+9)]`
`M^2 = [(5,8),(8,13)]`
`kM = [(k,2k),(2k, 3k)]`
`:. M^2 - kM - I_2 =0`
`[(5,8),(8,13)] - [(k, 2k),(2k , 3k)] - [(1,0),(0,1)] = [(0,0),(0,0)]`
`[(4-k,8 - 2k),(8-2k, 12-3k)] = [(0,0),(0,0)]`
4 - k = 0
k = 4
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